ORIGINAL PAPER
Compositional pattern producing networks: A novel
abstraction of development
Kenneth O. Stanley
Received: 13 April 2006 / Revised: 21 January 2007 / Published online: 10 May 2007
Springer Science+Business Media, LLC 2007
Abstract Natural DNA can encode complexity on an enormous scale. Researchers
are attempting to achieve the same representational efficiency in computers by
implementing developmental encodings, i.e. encodings that map the genotype to the
phenotype through a process of growth from a small starting point to a mature form.
A major challenge in in this effort is to find the right level of abstraction of
biological development to capture its essential properties without introducing
unnecessary inefficiencies. In this paper, a novel abstraction of natural development,
called Compositional Pattern Producing Networks (CPPNs), is proposed. Unlike
currently accepted abstractions such as iterative rewrite systems and cellular growth
simulations, CPPNs map to the phenotype without local interaction, that is, each
individual component of the phenotype is determined independently of every other
component. Results produced with CPPNs through interactive evolution of two-
dimensional images show that such an encoding can nevertheless produce structural
motifs often attributed to more conventional developmental abstractions, suggesting
that local interaction may not be essential to the desirable properties of natural
encoding in the way that is usually assumed.
Keywords Evolutionary computation Representation Developmental encoding
Indirect encoding Artificial embryogeny Generative systems Complexity
1 Introduction
Representation is at the heart of artificial intelligence. Particularly when a problem
involves search, a good representation of the solution space can mean the difference
between success and failure. In evolutionary computation, as traditional fixed-length
K. O. Stanley (&)
School of Electrical Engineering and Computer Science, University of Central Florida,
4000 Central Florida Blvd., Orlando, FL 32816-2362, USA
e-mail: kstanley@cs.ucf.edu
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DOI 10.1007/s10710-007-9028-8
genomes and direct encodings reach their limits, the importance of representation
has moved to the forefront of research. Meanwhile, biology remains a potent
reminder of how far there is to go. In biology, the genes in DNA represent
astronomically complex structures with trillions of interconnecting parts, such as the
human brain [1–3]. Yet DNA does not contain trillions of genes; rather, somehow
only 30,000 genes encode the entire human body [4].
There is thus reason to believe that the discovery of systems as complex as
humans is only possible through extraordinarily efficient encoding, as seen in
nature. A key process in natural encoding is development, in which DNA maps to
the mature phenotype through a process of growth that builds the phenotype over
time. Development facilitates the reuse of genes because the same gene can be
activated at any location and any time during the development process. Thus a small
set of genes can encode a much larger set of structural components.
This observation has inspired an active field of research in artificial developmental
encodings [5–8]. The aim is to find the right abstraction of natural development for a
computer running an evolutionary algorithm, so that it can begin to discover
complexity on a natural scale. Abstractions range from low-level cell chemistry
simulations to high-level grammatical rewrite systems [8]. A common facet of such
abstractions is that the state of an individual phenotypic component at one moment in
development affects the states of components in the same vicinity in the future, that is,
development unfolds through local interactions. Because no abstraction so far has
come close to discovering the level of complexity seen in nature, much interest
remains in identifying the properties of abstractions that give rise to efficient encoding.
This paper introduces a novel abstraction of natural development that breaks the
strong tradition of local interaction and temporal unfolding in developmental
encoding research. Yet it is nevertheless demonstrated that it captures several
essential characteristics of such encoding. The fundamental insight behind this new
encoding, called Compositional Pattern Producing Networks (CPPNs), is that it is
possible to directly describe the structural relationships that result from a process of
development without simulating the process itself. Instead, the description is
encoded through a composition of functions, each of which is based on observed
gradient patterns in natural embryos.
Because CPPNs are structurally similar to artificial neural networks, they can
right away take advantage of existing effective methods for evolving neural
networks. In particular, the Neuroevolution of Augmenting Topologies (NEAT)
method evolves increasingly complex neural networks over generations [9–11]. In
this paper, with only slight adjustment, NEAT is modified to create CPPN–NEAT,
which evolves increasingly complex CPPNs. In this way, it is possible to evolve
increasingly complex phenotype expression patterns, complete with symmetries and
regularities that are elaborated and refined over generations.
The main contribution of this paper is to establish CPPNs as a legitimate
abstraction of natural developmental encoding. To provide evidence for this claim, a
novel experimental approach to analyzing the properties of genetic encodings is
introduced: CPPN–NEAT-based interactive evolutionary computation (IEC), in
which a human select the parents of each new generation, is used to produce
examples of several fundamental structural motifs and elaborations of nature.
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Symmetry, reuse, reuse with variation, preservation of regularities, and elaboration
of existing regularities all are demonstrated and capitalized on by CPPN–NEAT,
validating it as a promising new abstraction of natural developmental encoding, and
one that is able to evolve increasingly complex patterns.
While the primary conclusion is simply that CPPNs are legitimate abstractions of
developmental encoding, the ramifications of this conclusion are significant.
Admitting a new class of encoding that lacks classic temporal unfolding and local
interaction expands the scope of developmental encoding research and suggests
possible new directions for the field. Perhaps most significantly, if similar motifs
can be produced with and without local interaction, the question arises whether local
interaction is, at a high level, essential to efficient encoding, or whether it is rather
only an artifact of the constraints imposed by physics in nature.
The next section provides background on the role of development in both natural
evolution and artificial evolutionary algorithms. Section 3 then details the CPPN
approach, and how CPPN–NEAT evolves increasingly complex patterns. Finally,
Sect. 4 explains the experimental approach and discloses results, followed by a
discussion in Sect. 5.
2 Background
This section introduces important concepts in developmental encoding, starting with
a review of prior computational abstractions. Following this review, typical patterns
produced by natural development are discussed, providing context for evaluating the
validity of different abstractions. Finally, an important process in natural evolution
called complexification, which also occurs in the experiments in this paper, is
described.
2.1 Artificial developmental encodings
The apparent connection between development and complexity in biology has
inspired significant research into artificial developmental encoding in recent years
[5–7, 12–37]. Just as a biological embryo starts from a single cell and through a
series of genetic instructions achieves structures of astronomical complexity,
artificial developmental encodings strive to map an artificial genome to a
comparatively more complex phenotype through a series of steps that grow a
small starting structure into a mature form.
Development makes such representational efficiency possible by allowing genes
to be reused in the process of assembling the phenotype. Without such reuse, the
genotype would need to be as complex as the phenotype, potentially including
millions or even trillions of separate genes, an intractable search space. Through
reuse the number of genes can be orders of magnitude fewer than the number of
structural units in the phenotype, making search for extremely complex structures
practical. For example, there are numerous receptive fields in the human visual
cortex, each of which is encoded from the same genes. Thus, a small number of
genes can encode for a large number of structures. As the brain develops during
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embryogenesis, each time a receptive field is built, a similar set of genes is activated
[38, 39]. In this way, development and reuse are complementary partners in the
representation of complexity. While factors such as the environment and its
interaction with development affect the success of evolutionary search as well, the
encoding’s efficiency provides a significant advantage.
Artificial developmental encodings attempt to exploit the relationship between
reuse and complexity in a similar way to nature. However, because computers differ
from the natural world and because it is not necessary to simulate every facet of a
biological process in order to capture its essential properties, finding the right level
of abstraction remains an open problem. Therefore, several levels of abstraction
have been explored in recent years. These range from low-level cell chemistry
simulations to higher-level grammatical approaches.
Cell chemistry methods simulate the local interactions among chemicals and
genes inside and between cells during embryogenesis [6, 12–20, 24–26, 28, 31–33,
37, 40, 41]. These methods follow the philosophy that the essential functions that
allow development to yield significant complexity are located in the physical
interactions that occur among proteins and cells in a developing embryo. Thus, cell
chemistry approaches evolve genes that produce simulated proteins that diffuse and
react as genotype maps to phenotype through a process of growth. The networks
formed by genes that send signals back and forth through their protein products are
called gene regulatory networks (GRNs). GRNs are often explicitly simulated in
cell chemistry methods [14, 16, 17].
In contrast, grammatical approaches simulate development at a higher level of
abstraction by evolving sets of rewrite (i.e. symbol replacement) rules [7, 21–23, 27,
29, 30, 34–36, 42]. When applied iteratively these rules grow a final structure from a
single starting symbol. Each replacement occurs at the locality of the symbol to be
replaced within the growing phenotype. Thus, local interaction and temporal
unfolding also control the growth of phenotypes through grammars.
Both approaches have produced significant results, including simulated three-
dimensional body morphologies and locomotion [7, 15], neural networks with
repeating structures [21, 27], and physical structures with self-similarity [7, 17].
However, no approach has achieved complexity even close to that seen in nature.
Thus, the search for powerful developmental encodings continues [8]. Expanding
the scope of developmental encoding to include novel abstractions opens up new
opportunities for such exploration.
The next section discusses important characteristics of developmental patterns.
2.2 Patterns of development
Development produces patterns and evolution produces sequences of patterns over
generations. Patterns include regularities, and regularities are what make reuse
possible. Without regularity, the same information could not produce different parts
of the same phenotype, removing much of the advantage of development. This
section enumerates a set of general characteristics of patterns observed in natural
organisms that can also be sought in artificially evolved phenotypes.
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Identifying the general characteristics of natural patterns is an important
prerequisite to describing how such patterns can be generated algorithmically. Both
Turing [37] and Lindenmayer [29] were initially inspired by the patterns they
observed in nature before they attempted to describe how those patterns could be
generated. Turing eventually proposed his reaction diffusion model,which
successfully produces patterns similar to those seen on sea shells and animal pelts,
and Lindenmeyer invented L-systems, which grow accurate plant-like morpholog-
ies. Thus, by identifying the common general properties of patterns in nature, it
becomes more clear for what phenomena artificial systems must account. The
following list describes both patterns present in individual organisms, and the way
those patterns change over generations.
• Repetition: Multiple instances of the same substructure is a hallmark of
biological organisms. From cells throughout the body to neurons in the brain, the
same motifs occur over and over again in a single organism. Repetition in the
phenotype is also called self-similarity [6].
• Repetition with variation: Frequently, motifs are repeated yet not entirely
identical. Each vertebrae in the spine is similar, yet they each have slightly
different proportions and morphologies [3]. Similarly, human fingers repeat a
regular pattern, yet no two fingers on the same hand are identical. Repetition
with variation is abundant throughout all of natural life.
• Symmetry: Often repetition occurs through symmetry, as when the left and right
sides of a body are identical mirror images in classic bilateral symmetry.
• Imperfect symmetry: While an overall symmetric theme is observable in
many biological structures, they are nevertheless generally not perfectly
symmetric. Such imperfect symmetry is a common feature of repetition with
variation. The human body, while overall symmetric, is not equivalent on both
sides; some organs appear only on one side and one hand is usually dominant
over the other.
• Elaborated regularity: Over many generations, regularities are often elaborated
and exploited further [43]. For example, the bilaterally symmetric fins of early
fish eventually became the arms and hands of mammals, displaying some of the
same regularities [44].
• Preservation of regularity: Over generations, established regularities are often
strictly preserved. Bilateral symmetry does not easily produce three-way
symmetry, and four-limbed animals rarely produce offspring with a different
number of limbs, even as the limb design itself is elaborated.
Using this list, phenotypes and lineages produced by artificial encodings can be
analyzed according to their natural characteristics, giving an indication whether a
particular encoding is capturing essential properties and capabilities of natural
development. The characteristics in this section are employed to interpret
experimental results reported in Sect. 4.
The next section describes a process through which the patterns represented by a
set of genes can become increasingly complex.
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